We present a coarse-grained model for the dynamics of living polymer
solutions which explicitly includes solvent hydrodynamics. We show that
lamellar and columnar structures emerge when the solution is subjected
to simple shear. In the absence of shear, the model predicts a fluid-gel
transition as a function of polymer concentration. At a threshold
concentration, the self-intermediate scattering function indicates Zimm-
like dynamics at large wave vectors and diffusive dynamics at small wave
vectors. The kinetics of scission and recombination clearly demonstrates
the existence of mean field and diffusion controlled regimes for the
dynamics of living polymers at low and high concentrations respectively.